Model order reduction of thermo-mechanical models with parametric convective boundary conditions: focus on machine tools
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ORIGINAL PAPER
Model order reduction of thermo-mechanical models with parametric convective boundary conditions: focus on machine tools Pablo Hernández-Becerro1,2
· Daniel Spescha1
· Konrad Wegener2
Received: 22 April 2020 / Accepted: 7 September 2020 © The Author(s) 2020
Abstract Thermo-mechanical finite element (FE) models predict the thermal behavior of machine tools and the associated mechanical deviations. However, one disadvantage is their high computational expense, linked to the evaluation of the large systems of differential equations. Therefore, projection-based model order reduction (MOR) methods are required in order to create efficient surrogate models. This paper presents a parametric MOR method for weakly coupled thermo-mechanical FE models of machine tools and other similar mechatronic systems. This work proposes a reduction method, Krylov Modal Subspace (KMS), and a theoretical bound of the reduction error. The developed method addresses the parametric dependency of the convective boundary conditions using the concept of system bilinearization. The reduced-order model reproduces the thermal response of the original FE model in the frequency range of interest for any value of the parameters describing the convective boundary conditions. Additionally, this paper investigates the coupling between the reduced-order thermal system and the mechanical response. A numerical example shows that the reduced-order model captures the response of the original system in the frequency range of interest. Keywords Parametric model order reduction · Thermo-mechanical model · Thermal error · Precision engineering · Machine tools
1 Introduction Machine tools, such as milling machines, grinding machines, or lathes, are complex mechatronic systems and key components in the manufacturing process. Increasing the precision of machine tools enables to manufacture more accurate parts required in many engineering applications. Among the different error sources limiting the precision of machine tools, thermally induced deviations are the main contributor to geometric errors in manufactured parts, as stated by Mayr et al. [18]. During the manufacturing process, the temperature distribution of machine tools is inhomogeneous and varies
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Pablo Hernández-Becerro [email protected] Daniel Spescha [email protected] Konrad Wegener [email protected]
1
inspire AG, Technoparkstrasse 1, 8005 Zurich, Switzerland
2
Institute of Machine Tool and Manufacturing, ETH Zurich, Leonhardstrasse 21, 8092 Zurich, Switzerland
over time, leading to deformations of the structural parts. Internal and external sources are responsible for the timevarying temperature distribution, as summarized by Bryan [13]. Internal sources refer to heat losses at the machine elements during the manufacturing process, such as friction at the bearings. External sources refer to the surroundings of the machine tool, such as fluctuations of the environmental temperature of the workshop. Virtual prototypes are a great asset to improve the ther
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